Perhaps Rodrygo doesn't fit in Xabi Alonso's pattern and this is common to happen to player(s) when a new coach comes into a club. Rodrygo just 24 is to me too young to take his career to the Saudi Pro league, and I agree, Arsenal won't be a favourable place for him even if Arsenal can afford his fees. Where I will love to see him play is PSG or Bayern Munich.
Every coach have their pattern of play, when they come into a new team with different players they never coach before, they do make some changes by choosing the players they want and make the rest of the players feel useless in the squad that is exactly what is happening to Rodrigo in Real Madrid as we speak.
Alonso said that he was going to give him playing time, but with the few matches he has already coached, it seems like he have an entire different pattern that have no space for Rodrigo in his squad that’s why Alonso made it clear that he can leave if better offer is submitted for him. Arsenal, PSG, and Manchester City are willing to sign him, one of them might be victorious if Saudi Arabian teams don’t pump in too much money to get him from Real Madrid.